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Numerical Simulation of the Cleaning Process of Microchannel by an External Flow

Boris S. Maryshev, Lyudmila S. Klimenko

TL;DR

The paper studies cleaning of a rectangular microchannel clogged by wall-adhered impurity particles under a pressure-driven, low-Reynolds-number flow. It develops a two-dimensional Stokes-flow model with Brownian diffusion and a random-walk particle transport framework, including a detachment criterion where viscous and random forces overcome van der Waals adhesion. Key findings show three cleaning regimes determined by the ratio of thermal stress $\sigma_t$ to adhesion stress $\sigma_V$, plus resonance-like effects under time-modulated flow that can drastically alter cleaning times. The results offer quantitative predictions of cleaning time, flow rate, and gap evolution, and suggest flow modulation as a practical control strategy for microfluidic cleanup.

Abstract

This paper describes the problem of drift of solid non-interacting particles in a microchannel, which can stick to its walls under the action of the van der Waals forces and break away from the wall due to thermal noise and viscous stresses arising from the flow. The pressure drop is given between the channel inlet and outlet. At the initial moment of time, the channel walls are contaminated with adhered particles, i.e. the walls are uneven, which affects the formation of the flow structure through the channel. Over time, under the action of viscous stresses and thermal noise, the particles break away from the channel walls, causing its cleaning. The interaction of the detached particles with the flow is taken into account in the Stokes approximation. In addition, the model takes into account random particle motion caused by diffusion. The problem is solved numerically within the framework of the random walk model. The evolution of the liquid flow in the channel during its cleaning is obtained: stream function, pressure, and vorticity fields. The dependencies of the volume occupied by settled particles, the flow rate through the channel and the channel gap on time are determined for different values of the interaction force between particles and channel wall. The estimations of the channel cleaning time are obtained and discussed. The possibility of control the cleaning process by the modulation of liquid flux through the channel is investigated. It is shown that resonance phenomena can be observed. The dependencies of cleaning time on the modulation amplitude and frequency is obtained and studied. It is shown that changing the modulation parameters leads to a significant change in the cleaning time and helps control the cleaning process.

Numerical Simulation of the Cleaning Process of Microchannel by an External Flow

TL;DR

The paper studies cleaning of a rectangular microchannel clogged by wall-adhered impurity particles under a pressure-driven, low-Reynolds-number flow. It develops a two-dimensional Stokes-flow model with Brownian diffusion and a random-walk particle transport framework, including a detachment criterion where viscous and random forces overcome van der Waals adhesion. Key findings show three cleaning regimes determined by the ratio of thermal stress to adhesion stress , plus resonance-like effects under time-modulated flow that can drastically alter cleaning times. The results offer quantitative predictions of cleaning time, flow rate, and gap evolution, and suggest flow modulation as a practical control strategy for microfluidic cleanup.

Abstract

This paper describes the problem of drift of solid non-interacting particles in a microchannel, which can stick to its walls under the action of the van der Waals forces and break away from the wall due to thermal noise and viscous stresses arising from the flow. The pressure drop is given between the channel inlet and outlet. At the initial moment of time, the channel walls are contaminated with adhered particles, i.e. the walls are uneven, which affects the formation of the flow structure through the channel. Over time, under the action of viscous stresses and thermal noise, the particles break away from the channel walls, causing its cleaning. The interaction of the detached particles with the flow is taken into account in the Stokes approximation. In addition, the model takes into account random particle motion caused by diffusion. The problem is solved numerically within the framework of the random walk model. The evolution of the liquid flow in the channel during its cleaning is obtained: stream function, pressure, and vorticity fields. The dependencies of the volume occupied by settled particles, the flow rate through the channel and the channel gap on time are determined for different values of the interaction force between particles and channel wall. The estimations of the channel cleaning time are obtained and discussed. The possibility of control the cleaning process by the modulation of liquid flux through the channel is investigated. It is shown that resonance phenomena can be observed. The dependencies of cleaning time on the modulation amplitude and frequency is obtained and studied. It is shown that changing the modulation parameters leads to a significant change in the cleaning time and helps control the cleaning process.

Paper Structure

This paper contains 4 sections, 20 equations, 15 figures.

Table of Contents

  1. Introduction
  2. Problem statement
  3. Results and discussions
  4. Conclusion

Figures (15)

  • Figure 1: The sketch of the problem
  • Figure 2: Algorithm of the channel clogging calculation
  • Figure 3: Algorithm of the cleaning calculation
  • Figure 4: Position of the walls of the channel contaminated with impurity in different time moments, the area occupied by impurity particles is shaded in black
  • Figure 5: The dependencies of fluid flux $J$ on time for different values of thermal noise stress $\sigma_t$ which is indicated in legend. The van der Waals force stress value is $\sigma_V=0.3$.
  • ...and 10 more figures